PSY 311 1st Edition Lecture 6Outline of Last Lecture I. Standard Deviation II. Z- Scores a. Z tables III. Sampling Distribution a. Standard errorIV. Hypothesis Testing (5 steps) a. Null hypothesisb. Alternative hypothesisV. Experimenters Decisiona. Type 1 error b. Type 2 error Outline of Current Lecture I. Why can’t we use z a. William Gossett II. Student’s t statistic a. T distribution III. Hypothesis Testing IV. Effect size – Cohen’s d Current Lecture : Introduction to the t statistic I. Why cant we use z? - The z statistic is used when we know the value of the population standard deviation , and thus the value of standard error m - This is very rare - William Gossett - Was the person who came up with the t statistic. His job was to sample beer for the population and make conclusions about the product. He had a problem using the z statistic because ofdifferent errors. Since he was working for a company he could not publish his findings as his own so he published them under the name student. II. Student’s t statistic - When we don’t know the values of m we must estimate it by using the estimated standard error of the sample (sm) - Sm = s/n or (s²/n)- The one that we are using is (s²/n) which means that you square root the variance (s²) divided by the sample size (n) - The formula for the t statistic is t = (M-µ)/sm- The t distribution changes based on the degrees of freedom and it is shorter and wider than the z distribution which is normal- The larger the sample size the closer you are going to be to the z distribution or a normal distribution - Higher df ( degrees of freedom) = closer to normal distribution - Remember df= n-1 III. Hypothesis Testing 5 steps: 1. State the hypothesis 2. Locate critical region - If m is known use z table - If m is unknown use t table 3. Collect data and compute test statistic - If m is known, calculate z statistic - If m is unknown, calculate t statistic 4. Make decision on null hypothesis 5. Report Finding T (df) = calculated value , p < or > the alpha value- Use < to denote a significant effect - Use > to denote non-significant effect IV. Effect Size – Cohen’s d - Estimated d = (M-µ)/s ( sample mean – population mean) / sample standard deviation - If d is :- 0.2 (small effect)- 0.5 ( medium effect)- 0.8 ( large